9,663 research outputs found
Towards concept analysis in categories: limit inferior as algebra, limit superior as coalgebra
While computer programs and logical theories begin by declaring the concepts
of interest, be it as data types or as predicates, network computation does not
allow such global declarations, and requires *concept mining* and *concept
analysis* to extract shared semantics for different network nodes. Powerful
semantic analysis systems have been the drivers of nearly all paradigm shifts
on the web. In categorical terms, most of them can be described as
bicompletions of enriched matrices, generalizing the Dedekind-MacNeille-style
completions from posets to suitably enriched categories. Yet it has been well
known for more than 40 years that ordinary categories themselves in general do
not permit such completions. Armed with this new semantical view of
Dedekind-MacNeille completions, and of matrix bicompletions, we take another
look at this ancient mystery. It turns out that simple categorical versions of
the *limit superior* and *limit inferior* operations characterize a general
notion of Dedekind-MacNeille completion, that seems to be appropriate for
ordinary categories, and boils down to the more familiar enriched versions when
the limits inferior and superior coincide. This explains away the apparent gap
among the completions of ordinary categories, and broadens the path towards
categorical concept mining and analysis, opened in previous work.Comment: 22 pages, 5 figures and 9 diagram
On some pro-p groups from infinite-dimensional Lie theory
We initiate the study of some pro-p-groups arising from infinite-dimensional
Lie theory. These groups are completions of some subgroups of incomplete
Kac-Moody groups over finite fields, with respect to various completions of
algebraic or geometric origin. We show topological finite generation for the
pro-p Sylow subgroups in many complete Kac-Moody groups. This implies abstract
simplicity of the latter groups. We also discuss with the question of
(non-)linearity of these pro-p groups.Comment: 16 page
Exploring Subexponential Parameterized Complexity of Completion Problems
Let be a family of graphs. In the -Completion problem,
we are given a graph and an integer as input, and asked whether at most
edges can be added to so that the resulting graph does not contain a
graph from as an induced subgraph. It appeared recently that special
cases of -Completion, the problem of completing into a chordal graph
known as Minimum Fill-in, corresponding to the case of , and the problem of completing into a split graph,
i.e., the case of , are solvable in parameterized
subexponential time . The exploration of this
phenomenon is the main motivation for our research on -Completion.
In this paper we prove that completions into several well studied classes of
graphs without long induced cycles also admit parameterized subexponential time
algorithms by showing that:
- The problem Trivially Perfect Completion is solvable in parameterized
subexponential time , that is -Completion for , a cycle and a path on four
vertices.
- The problems known in the literature as Pseudosplit Completion, the case
where , and Threshold Completion, where , are also solvable in time .
We complement our algorithms for -Completion with the following
lower bounds:
- For , , , and
, -Completion cannot be solved in time
unless the Exponential Time Hypothesis (ETH) fails.
Our upper and lower bounds provide a complete picture of the subexponential
parameterized complexity of -Completion problems for .Comment: 32 pages, 16 figures, A preliminary version of this paper appeared in
the proceedings of STACS'1
Fr\'echet completions of moderate growth old and (somewhat) new results
This article has two objectives. The first is to give a guide to the proof of
the (so-called) Casselman-Wallach theorem as it appears in Real Reductive
Groups II. The emphasis will be on one aspect of the original proof that leads
to the new result in this paper which is the second objective. We show how a
theorem of van der Noort combined with a clarification of the original argument
in my book lead to a theorem with parameters (an alternative is one announced
by Berstein and Kr\"otz). This result gives a new proof of the meromorphic
continulation of the smooth Eisenstein series
Remarks on Rational Points of Universal Curves
In this notes, we will give some remarks on the results in Rational points of
universal curves by Hain. In particular, we consider the universal curves
and the sections of their algebraic
fundamental groups.Comment: 14 pages. The section of the unipotent section conjecture in positive
characteristic has been removed from this version. It will be a separate
paper due to the nature of the conten
Composite Higgs models in disguise
We present a mechanism for disguising one composite Higgs model as another.
Allowing the global symmetry of the strong sector to be broken by large mixings
with elementary fields, we show that we can disguise one coset such that at low energies the phenomenology of the model is
better described with a different coset . Extra scalar
fields acquire masses comparable to the rest of the strong sector resonances
and therefore are no longer considered pNGBs. Following this procedure we
demonstrate that two models with promising UV-completions can be disguised as
the more minimal coset
The index complex of a maximal subalgebra of a Lie algebra.
Let M be a maximal subalgebra of the Lie algebra L. A subalgebra C of L is said to be a completion for M if C is not contained in M but every proper subalgebra of C that is an ideal of L is contained in M. The set I(M) of all completions of M is called the index complex of M in L. We use this concept to investigate the influence of the maximal subalgebras on the structure of a Lie algebra, in particular finding new characterisations of solvable and supersolvable Lie algebras
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